From 30f75f7bb2fbb9e7252f87aa4f5246fce7203150 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Daniel=20Kn=C3=BCttel?= Date: Wed, 11 Mar 2020 10:49:10 +0100 Subject: [PATCH] forgot some modulus there --- thesis/chapters/stabilizer.tex | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/thesis/chapters/stabilizer.tex b/thesis/chapters/stabilizer.tex index e2807ac..a33e363 100644 --- a/thesis/chapters/stabilizer.tex +++ b/thesis/chapters/stabilizer.tex @@ -261,11 +261,11 @@ and $s=0$ are obtained with probability $\frac{1}{2}$ and after choosing a $j \begin{equation} \begin{aligned} - P(s=0) &= \hbox{Tr}\left(\frac{I + g_a}{2}\ket{\psi}\bra{\psi}\right) \\ - &= \hbox{Tr}\left(\frac{I + g_a}{2}S^{(j)} \ket{\psi}\bra{\psi}\right)\\ - &= \hbox{Tr}\left(S^{(j)}\frac{I - g_a}{2}\ket{\psi}\bra{\psi}\right)\\ - &= \hbox{Tr}\left(\frac{I - g_a}{2}\ket{\psi}\bra{\psi}S^{(j)}\right)\\ - &= \hbox{Tr}\left(\frac{I - g_a}{2}\ket{\psi}\bra{\psi}\right)\\ + P(s=0) &= \left|\hbox{Tr}\left(\frac{I + g_a}{2}\ket{\psi}\bra{\psi}\right) \right|\\ + &= \left|\hbox{Tr}\left(\frac{I + g_a}{2}S^{(j)} \ket{\psi}\bra{\psi}\right)\right|\\ + &= \left|\hbox{Tr}\left(S^{(j)}\frac{I - g_a}{2}\ket{\psi}\bra{\psi}\right)\right|\\ + &= \left|\hbox{Tr}\left(\frac{I - g_a}{2}\ket{\psi}\bra{\psi}S^{(j)}\right)\right|\\ + &= \left|\hbox{Tr}\left(\frac{I - g_a}{2}\ket{\psi}\bra{\psi}\right)\right|\\ &= P(s=1) \end{aligned} \notag